Question

Three friends all have ages that are consecutive integers. The sum of their ages is 180. What is the age of the oldest?

Answer 1

n= youngest
n+1= middle friend (by age)
n+2 = oldest

n + n + 1 + n + 2 = 180 (the sum of their ages = 180)

Combine like terms
3n + 3 = 180

Now subtract 3 from each side of the equation

3n + 3 - 3 = 180 -3
3n = 177

Now divide both sides of the equation by 3
n= 59 n + 1 = 60 and n + 2=61 Ages are 59, 60, 61

Another way 180 ÷ 3 = 60. So 60 + 60 + 60 =180 Take one from one of the 60s and add it to one of the others and you will also get 59,60 and 61.

Answer 2

Age (A) = n = 59

Age (B) = n+1 = 60

Age (C) = n+2 = 61

*The oldest is Age (C).

---------

n+(n+1)+(n+2)=180

n+n+1+n+2=180

3n+3=180

3(n+1)=180

n+1=60

n=59

-----------

The answer is: 61 years old.